How to Identify the best method to impute the study-specific standard deviation for meta-analyses on skewed endpoints : a simulation approach

Meta-analyses of continuous endpoints are generally supposed to deal with normally distributed data. In this context, two treatment groups are generally compared looking at the difference in their means and the pooled estimate of the treatment effect typically relies on means and standard deviations (SDs) [1]. However, if the outcome distribution is skewed, some authors correctly report the median together with the corresponding quartiles, whereas others still provides means and standard deviations [2]. This poses a challenge for those researchers typically carrying out meta-analyses on skewed continuous outcomes. At the simpler level, an interest emerged as to the opportunity and the way to approximate study-specific means and SDs from study-specific medians and quartiles. In the present work, we compare four available methods to deal with the issue of how to approximate the study-specific standard deviation, in the case where the study-specific mean is expected to be fairly approximated by the study-specific median: 1) conservative SD, 2) less conservative SD, 3) mean SD, or 4) interquartile range. The reference set-up for comparison is the traditional one where pooled estimates were derived from study-specific means and SDs. We performed simulated meta-analyses on 6 dataset clusters of 15, 30, 50, 100, 500, and 1000 datasets respectively. Each dataset is composed by the same number of subjects in the treatment and control groups. Subjects were iteratively generated from one of the following 7 scenarios: 5 theorical continuous distributions (Normal, Normal (0,1), Gamma, Exponential, Bimodal) and 2 real-life distributions of Intensive Care Unit (ICU) stay and hospital stay from an Italian observational study on 7,471 patients with cardiovascular disease. For each simulation, we calculated the pooled estimates assembling the study-specific medians and, in turn, all four SD approximations. We evaluated the difference among standardized estimates with a repeated measures model using the MIXED PROCEDURE implemented into SAS software. We also provided a graphical evaluation of the standardized differences. To show which imputation method produced the best estimate, we ranked those differences and calculated the rate at which each estimate appeared as the best, second-best, third-best, or fourth-best. It emerged that the best pooled estimate for the overall mean and SD is provided by the approximation with the median and IQR or by the median and the SD conservative estimate. Furthermore, these methods showed the lowest mean difference (mean standardized estimates: 4.5±3.5 for method 1 and 4.5±2.2 for method 4, respectively) (p<0.05). The less conservative approximation of SD appear to be the worst method, exhibiting a significant difference from the reference method at the 90% confidence level. The method that ranked first most frequently is “IQR” (55%), particularly when data were generated according to the Standardized Normal, Gamma, and Exponential distributions. The second best is the “Conservative SD” method (36%), particularly for data from a bimodal distribution and for the ICU stay variable. In conclusion, there seems to be emerging evidence in favour of the practice of approximating the study-specific missing values of mean and SD with the corresponding values for median and IQR.